20E_sheet3

20E_sheet3 - • The Stokes’ Theorem says that: ± ∂ S...

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FACT SHEET FOR 20E FINAL 1. From Chapter 8 The Divergence Theorem in 3D says that: ±± S ± F · ˆ n dS = ± ± ± Ω ∇· ± F dxdydz , where S = Ω is the closed surface that bounds the domain Ω R 3 . Here ˆ n points to the exterior of Ω. The Green’s Theorem says that: ± Ω ± F · = ±± Ω ( x F 2 - y F 1 ) dxdy , where Ω is the closed curve that bounds the domain Ω R 2 . Here the orientation of Ω in the path integral is counter-clockwise.
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Unformatted text preview: • The Stokes’ Theorem says that: ± ∂ S ± F · d² = ± ± S ( ∇× ± F ) · ˆ n dS , where ∂ S is the boundary curve of the surface patch S , and the orientation of ∂ S in the path integral as well as the direction of ˆ n obeys the “right-hand-rule”. This should be understood as a generalization of the Green’s theorem. 1...
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This note was uploaded on 03/16/2010 for the course MATH 223B taught by Professor Staff during the Spring '09 term at Arizona.

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